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Simplify this expression . With each step. please (x2 - x - 2)/(x2 + 5x + 4)

User Amritha
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1 Answer

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Answer:

I hope dis helps

Explanation:

Simplify

x2 + 5x + 4

Trying to factor by splitting the middle term

1.1 Factoring x2 - x - 2

The first term is, x2 its coefficient is 1 .

The middle term is, -x its coefficient is -1 .

The last term, "the constant", is -2

Step-1 : Multiply the coefficient of the first term by the constant 1 • -2 = -2

Step-2 : Find two factors of -2 whose sum equals the coefficient of the middle term, which is -1 .

-2 + 1 = -1 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -2 and 1

x2 - 2x + 1x - 2

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (x-2)

Add up the last 2 terms, pulling out common factors :

1 • (x-2)

Step-5 : Add up the four terms of step 4 :

(x+1) • (x-2)

Which is the desired factorization

Trying to factor by splitting the middle term

1.2 Factoring x2+5x+4

The first term is, x2 its coefficient is 1 .

The middle term is, +5x its coefficient is 5 .

The last term, "the constant", is +4

Step-1 : Multiply the coefficient of the first term by the constant 1 • 4 = 4

Step-2 : Find two factors of 4 whose sum equals the coefficient of the middle term, which is 5 .

-4 + -1 = -5

-2 + -2 = -4

-1 + -4 = -5

1 + 4 = 5 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 1 and 4

x2 + 1x + 4x + 4

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (x+1)

Add up the last 2 terms, pulling out common factors :

4 • (x+1)

Step-5 : Add up the four terms of step 4 :

(x+4) • (x+1)

Which is the desired factorization

Canceling Out :

1.3 Cancel out (x+1) which appears on both sides of the fraction line.

Final result :

x - 2

—————

x + 4

User Clee
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